Winch pull for a 1,200 kg car up a 10° ramp (μ = 0.02)

Answer: tension (with friction) = 2,275.272 N (tension (frictionless) 2,043.488 N).

What we know

  • Mass: 1200 kg
  • Incline angle: 10°
  • Friction coefficient (μ): 0.02

μ here is a rolling-resistance coefficient for a car on its wheels.

Step by step

Given
m = 1200 kg, θ = 10°, μ = 0.02
Formula
T = m·g·(sin θ + μ·cos θ)
Substitute
T = 1200 × 9.80665 × (sin 10 + 0.02 × cos 10)
Result
T = 2,275.272 N

All results

Tension (with friction)2,275.272 N
Tension (frictionless)2,043.488 N

Open the incline tension calculator with these numbers → and change any of them.

The physics

A rope pulling a block up a slope has to fight two things: the component of gravity acting down the incline (mg·sin θ) and kinetic friction (μ·mg·cos θ), which also points down the slope while the block moves up. Add them and, for a rope parallel to the surface, T = m·g·(sin θ + μ·cos θ).